Question

What is an equation of the line that passing through the points (-2, -5) and (4, 7) ?

Answer 1

Answer:

$y=2x-1$

Step-by-step explanation:

Use the slope-intercept formula: $y=mx+b$ where m is slope and b the y-intercept.

$(-2,-5)(4,7)$

Use the slope formula for when you have two points:

$\frac{y(2)-y(1)}{x(2)-x(1)}=\frac{rise}{run}$

Rise over run is the change in the y-axis over the change in the x-axis. Insert values:

$\frac{7-(-5)}{4-(-2)}$

Simplify parentheses (negative+negative=positive)

$\frac{7+5}{4+2}$

Simplify

$\frac{12}{6}=2$

2 is the slope:

$y=2x+b$

Now use one of the points to find the y-intercept by substituting the x and y values into the equation. Solve for b:

(4,7)

$y=2x+b\\7=2(4)+b$

$7=8+b\\7-8=8-8+b\\7-8=b\\-1=b\\b=-1$

The y-intercept is -1. Insert into the equation. Change the + symbol to -:

$y=2x-1$

Done.