Answer:
(-5, 0)
Step-by-step explanation:
To find the x-intercept, I found the equation of the line first.
The equation of the line: y = mx + c where m is the slope of the line and c is the y-intercept.
Slope = [tex]\frac{rise}{run}[/tex]
= [tex]\frac{-33-(-22)}{52-33}[/tex]
= [tex]\frac{-33+22}{52-33}[/tex]
Slope = [tex]\frac{-11}{19}[/tex]
Thus, the slope of the line is -[tex]\frac{11}{19}[/tex].
To find the y-intercept, we just have to put the slope of the line into an ordered pair.
y = mx + c
-22 = -[tex]\frac{11}{19}[/tex](33) + c
-22 = -19[tex]\frac{2}{19}[/tex] + c
c = -22 + 19[tex]\frac{2}{19}[/tex]
c = -[tex]\frac{55}{19}[/tex]
Thus, the y-intercept is -[tex]\frac{55}{19}[/tex].
Thus, the equation of the line is: y = -[tex]\frac{11}{19}[/tex]x - [tex]\frac{55}{19}[/tex]
To find the x-intercept, we just have to put the equation of the line where y = 0.
y = -[tex]\frac{11}{19}[/tex]x - [tex]\frac{55}{19}[/tex]
0 = -[tex]\frac{11}{19}[/tex]x - [tex]\frac{55}{19}[/tex]
[tex]\frac{55}{19}[/tex] = -[tex]\frac{11}{19}[/tex]x
Multiply both sides by 19 to remove the fraction.
55 = -11x
x = 55 ÷ -11
x = -5
Thus, the x-intercept is -5.
You can draw out the line itself using the ordered pairs to find the x-intercept as well :)
