Linear Equations

1. Linear Equations In the warm-up, you were able to write an equation knowing only the slope and the y-intercept. If you have these two things, you can write an equation. Sometimes you will be given the slope but not the y-intercept. You can still write the equation if you are also given a point that lies on the line. If you are given the slope and a point on the line, you can find the y-intercept. For example, what is the equation of a line with a slope of 3 that goes through the point (2,8)? Which piece of information do we already have-the slope or y-intercept? The slope = 3. So, m= 3. y = 3x + b

2. Linear Equations y = 3x + b If we knew what b was equal to, we would be able to complete the equation. We can find b because we have a point that lies on the line−(2, 8). Since any point represents an x and a y, we can just substitute those values in for x and y in the equation. y = 3x + b 8 = 3(2) + b Now, we have one equation with one variable that can be solved. 8 = 6 + b 2 = b Now, we have the slope and the y-intercept so we can complete the equation. y = 3x + 2

3. Linear Equations What is the equation of a line with a slope of 2 that goes through the point (4,12)? Since we already know the slope, we can start with y = 2x + b. Now, we just have to find the y-intercept. Just substitute the point given to us in for x and y. 12 = 2(4) + b 12 = 8 + b 4 = b So, my equation is y = 2x + 4

4. Linear Equations What is the equation of a line with a slope of 4 that goes through the point (1,9)?