Question

What is the equation of the line that has a slope of 4 and passes through the point (-1, 4)?

Answer 1

Answer:

$y=4x+8$

Step-by-step explanation:

Linear equations are typically organized in slope-intercept form:

$y=mx+b$

Here's what the variables mean:

$y$ = the y-coordinate

$m$ = the slope of the line

$x$ = the x-coordinate

$b$ = the y-intercept (the value of y where the line crosses the y-axis)

Because the slope of the line is 4, we can plug that into our equation as $m$:

$y=4x+b$

Now, all we have to do is solve for $b$, the y-intercept. We can do this by plugging the point (-1, 4) into the equation as $x$ and $y$.

$4=4(-1)+b$

Solve the equation

$4=4(-1)+b\\4=-4+b$

Add 4 to both sides to isolate $b$

$4+4=-4+b+4\\8=b$

Therefore, $b$, or the y-intercept, is equal to 8.

Now, when we plug the y-intercept into our equation, we get:

$y=4x+8$

I hope this helps!

Answer 2

Answer:

y = 4x + 8

Step-by-step explanation:

Plug x = -1 into each of the equations, and see which one results in y = 4.

The first equation will be the only correct answer.

y = 4x + 8

y = -4 + 8

y = 4