Interpreting Lines:This is an introduction to drawing lines when given the slope and the y-intercept in an equation form. Remember that the y-intercept is where the graph crosses the y-axis; this is where we usually start. First, find the y-intercept, then determine the slope. For now, just focus on whether the slope is positive or negative. Show
Here are the variables we will start using in our function:
The equation is y = mx + b. The x and y variables remain as letters, but m and b are replaced by numbers (ex: y = 2x + 4, slope = 2 and y-intercept = 4). The following video will show a few examples of understanding how to use the slope and intercept from an equation. Video Source (03:53 mins) | Transcript y = mx + b This equation is called the slope-intercept form because the two numbers in the equation are the slope and the intercept. Remember, the slope (m) is the number being multiplied to x and the intercept (b) is the number being added or subtracted. Additional Resources
Practice Problems
You need two pieces of information to find the equation of the lineYou have two options for writing the equation of a line: point-slope form and slope-intercept form. Hi! I'm krista. I create online courses to help you rock your math class. Read more. Both of them require that you know at least two of the following pieces of information about the line:
If you know any two of these things, you can find the equation of the line. Point-slope form The equation of a line in point-slope form can be written as ???y-y_1=m(x-x_1)??? In this form, ???(x_1,y_1)??? is a point on the line, and ???m??? is the slope. To use this form when you know two points on the line but you don’t know the slope, first find ???m??? using ???m=\frac{y_2-y_1}{x_2-x_1}??? Then simply plug the slope ???m??? and the coordinates of one point ???(x_1,y_1)??? into the point-slope form of the equation of a line. How to find the equation of a line in slope-intercept formTake the courseWant to learn more about Algebra 1? I have a step-by-step course for that. :)Equation of the line from the slope and a point on the lineExample Write the equation of the line in point-slope form. ???m=-\frac{1}{4}??? ???(-6,1)??? Since we’ve been given the slope of the line and a point on the line, we can use the point-slope form to find the equation of the line. We’ll plug ???m=-1/4??? and the coordinates of the point ???(-6,1)??? into the point-slope form of the equation of a line. ???y-y_1=m(x-x_1)??? ???y-1=-\frac{1}{4}(x-(-6))??? ???y-1=-\frac{1}{4}(x+6)??? Let’s try an example where we know two points on the line. You have two options for writing the equation of a line: point-slope form and slope-intercept form. Example Find the point-slope form of the equation of the line that passes through the points ???(-2,-4)??? and ???(3, 5)???. Use ???(-2,-4)??? for ???(x_1,y_1)???. First, we need to find the slope of the line. It’s best to label the points before we plug them into the slope formula. We’ll say ???(-2,-4)=(x_1,y_1)??? ???(3,5)=(x_2,y_2)??? Plug these into the formula for the slope. ???m=\frac{y_2-y_1}{x_2-x_1}??? ???m=\frac{5-(-4)}{3-(-2)}??? ???m=\frac{9}{5}??? Next, substitute ???m=9/5??? and the coordinates of the point ???(-2,-4)??? into the equation ???y-y_1=m(x-x_1)???. If you know two or more points on the line, as we do in this problem, you can use the coordinates of any point on the line, and you’ll get a correct equation for the line. ???y-(-4)=\frac{9}{5}(x-(-2))??? ???y+4=\frac{9}{5}(x+2)??? Let’s try another example where we know two points on the line and need to find the equation of the line in point-slope form. Example Find the point-slope form of the equation of the line that passes through the points ???(4,2)??? and ???(6,3)???. We start by finding the slope. ???m=\frac{3-2}{6-4}=\frac{1}{2}??? Now plug in the slope and the coordinates of one of the points into the point-slope form of the equation of a line. We’ll use the point ???(4,2)???. Even though we could simplify this further (by distributing the ???1/2??? over the two terms inside the parentheses), we’d end up with something that isn’t in point-slope form, so we leave it as is. Get access to the complete Algebra 1 courseLearn mathAugust 30, 2020math, learn online, online course, online math, algebra, algebra 1, algebra i, equation of a line, slope-intercept form, slope, slope of a line, y=mx+b Which of the following is the equation of a line in slopeThe slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line. y-intercept is -2. c is the y-intercept. Therefore, the equation of the line is y = (2/3)x - 2.
Which of the following is the equation of a line in a slopeAnswer: The equation of the line that has a slope of 4 and a y-intercept of 2 is y = 4x + 2. Let's look into the steps below.
How do you write an equation in slopeTo change the equation into slope-intercept form, we write it in the form y=mx+b .
Which of the following is the equation of a line in slopeGraphing a Line Using Its Slope and y-Intercept
The equation of a line with a slope of m and a y-intercept of (0, b) is y = mx + b. To graph a line that is written in slope-intercept form: Plot the y-intercept on the coordinate plane.
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