Question

What is the equation of the line that goes through (-5,0) and (-4,4)

Answer 1

Answer:

$y=4x+20$

Step-by-step explanation:

To write an equation, use the slope-intercept equation:

$y=mx+b$

M is the slope and b is the y-intercept.

First, find the slope by using 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. Substitute values:

$(-5,0)(-4,4)\\(-5(x1),0(y1))\\(-4(x2),4(y2))\\\\\frac{4-0}{-4-(-5)}$

Simplify parentheses (two negatives make a positive) and simplify:

$\frac{4-0}{-4+5}\\\\\frac{4}{1}=4$

The slope, m, is 4. Insert this information into the equation:

$y=4x+b$

Now, take one of the points and insert into the slope-intercept formula:

$(-5,0)\\(-5(x),0(y))\\\\0=4(-5)+b$

Solve for b, the y-intercept. Simplify multiplication:

$0=-20+b$

Add 20 to both sides and simplify:

$0+20=-20+20+b\\20=b\\b=20$

The y-intercept, b, is 20. Insert this value into the equation:

$y=4x+20$

Done.