Question

What is the x-intercept of a line that passes through the point (3,4) and has a slope of 2?​

Answer 1

Answer:

(1,0)

Step-by-step explanation:

Hi there!

We want to find the x intercept of the line that passes through the point (3,4) and has a slope of 2

First, let's find the line

We are given both a slope, and a point. We can write the equation of the line in point-slope form, which is $y-y_1=m(x-x_1)$, where m is the slope and $(x_1, y_1)$ is a point

We do have everything needed to write the equation, let's just label everything to avoid confusion:

m=2

$x_1=3$

$y_1$=4

Now substitute those values as the variables that they represent into the equation:

$y-y_1=m(x-x_1)$

y-4=2(x-3)

Now we have the equation in slope-point form

The x intercept of the line is the value in which the line passes through the x axis. The value of y at this point is 0

So we can substitute y as 0 in the equation to find out the value of x:

y-4=2(x-3)

0-4=2(x-3)

Multiply

0-4=2x-6

Add 6 to both sides

0+2=2x

Simplify the left

2=2x

Divide both sides by 2

1=x

So the value of the x intercept is 1, also written as the point (1,0)

Hope this helps!