Answer:
(
2 , 5 ) and
(
26
/3 , 0
)
Step-by-step explanation:
Find the equation using the two points.
Use y
=
m
x
+
b to calculate the equation of the line, where m represents the slope and b represents the y-intercept.
To calculate the equation of the line, use the y
=
m
x
+
b format.
Slope is equal to the change in y over the change in x
, or rise over run.
The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).
[tex]m=\frac{y_{2-y_{1} } }{x_{2-y_{1} } }[/tex]
Substitute in the values of x and y into the equation to find the slope.
[tex]m=\frac{0-(5)}{\frac{2}{6} -(2)}[/tex]
Multiply the numerator and denominator of the complex fraction by 3
.
Finding the slope m
.
[tex]m=-\frac{3}{4}[/tex]
Find the value of b using the formula for the equation of a line.
[tex]b=\frac{13}{2}[/tex]
Find the x-intercepts.
To find the x-intercept(s), substitute in 0 for y and solve for x
.
[tex]0=-\frac{3}{4}x+\frac{13}{2}[/tex]
solve the equation
[tex]x=\frac{26}{3}[/tex]
x-intercept(s): [tex](\frac{26}{3},0)[/tex]
Find the y-intercepts.
To find the y-intercept(s), substitute in 0 for x and solve for y
.
[tex]0=-\frac{3}{4}*0+\frac{13}{2}[/tex]
[tex]y=\frac{13}{2}[/tex]
y-intercept(s): [tex](0,\frac{13}{2})[/tex]
