Geometry in High School

Question

What is the equation of the line that passes through (-3, 2) and is parallel to the graphed equation?

Answer 1

Hello, Stephanie,

I don't see the "graphed equation," nor any y= mx + b that would allow a calculation.

A parallel line would have the same slope, m. So your new line would be y = mx +b1, where b1 can be calculated after you have the slope, since we know (-3,2):

2 = m(-3) + b1

(You have the one place the line crosses, so put those values in the equation with the same slope, m, and then calculate b1.

Bob

Answer 2

Stephanie, can you post an image of the graphed equation? Your final result should be an equation with the same slope as the graphed line, and which also satisfies the condition f(-3) = 2

Assuming the graphed equation is linear, you can use the point-slope or slope-intercept methods to find the slope of the graphed equation:

Choose two points on the graph (x₁, y₁,) and (x₂, y₂) to find the slope:

slope = m = (y₂ - y₁) / (x₂ - x₁)

then substitute m and the point values (-3, 2,) into the point-slope formula for (x_p, y_p).

y - y_p = m*(x - (x_p)

y - 2 = m*(x - (-3)) = m*(x + 3);, distribute m to each value inside parentheses (x+3)

y -2 = m*x + 3*m, add 2 to each side of the equation for your result

y = m*x + 3*m +2

OR

use slope-intercept and substitute the values of (-3, 2,) for x and y respectively to find the value of b

y = m*x + b

2 = m*(-3) + b, where b = 3*m + 2 (same result as above)

y = m*x + 3*m + 2