Question

What is the equation of the line that passes through the point (4,-6) and has a slope of -5/2?

Answer 1

Answer:

y = (-5/2)X + 4

Step-by-step explanation:

we know that the equation of a line is y = mx + b

m = -5/2

so

y = -5/2x + b

to find b:

-6 = -10 + b

b = 4

so

y = (-5/2)X + 4

Answer 2

Answer:

Use the point-slope form of a linear equation:

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

where:

• $m$ = slope
• $(x_1,y_1)$ = point on line

Given:

• $m=-\dfrac52$
• $(x_1,y_1)=(4,-6)$

Substitute given information into the equation:

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

$\implies y-(-6)=-\dfrac52(x-4)$

$\implies y+6=-\dfrac52x+10$

$\implies y=-\dfrac52x+4$

Therefore, the equation of the line in different formats is:

$\textsf{slope-intercept form: }y=-\dfrac52x+4$

$\textsf{standard form: }5x+2y=8$