Write the equation of the line that has an x-intercept of -3 and passes through the point (-3, 7).

Question

i need the answer

Answer 1

Word Problems seem to give Algebra students the most trouble, but not to worry; this is rather simple.

 

First things first, in order to write the equation of a line, we need to know 2 things; Slope and Y-Intercept

 

we know that slope is defined as the change in y (Δy) over the change in x (Δx) or m = ∆y/∆x or (y₂-y₁)/(x₂-x₁)

 

we are given 2 points in this question (-3,7) and the x intercept, note that the x intercept is the point where the line crosses the x (Horizontal) axis and therefore the y value at that point is 0; thus our second point is (-3,0).

 

Using this information I will now calculate the value for the slope by plugging the respective values into the slope formula

 

I will let my first point (-3,7) be (x₁,y₁) and the second point (-3,0) be (x₂,y₂)

 

Thus, (0 - 7)/(-3 - (-3)) = m

 

m = -7/0, but wait, division by 0 is undefined, a vertical line,...what does that mean.

 

simply put, the slope is undefined and the result is a vertical line through the x values in this problem which is -3.  Also, note that this vertical line will never touch the y-axis and, therefore the y-intercept is non-existent for this problem

 

So, the equation we use is to encompass all x values at that undefined line X = -3 and we will see that this line will include the points (-3,0) and (-3,7)

 

Fell free to message is you need clarification.