Question

a line passes through the point (4 –6) and has a slope of -la1" title="\frac{5}{4}" alt="\frac{5}{4}" align="absmiddle" class="latex-formula">. which is the equation of the line

Answer 1

Answer:

$y = \frac{5}{4}x - 1$

Step-by-step explanation:

A line that passes through the point (4,-6) has a slope of 5/-4. Which of the following gives the equation of the line?

With the slope of 5/-4, and the ordered pair (4,-6) :  

let m = 5/-4 (slope),  

x1 = 4

y1 = -6

We can use those given values into the point-slope formula:

y - y1 = m(x - x1)

Plugging in those values will give you the answer:  

y - (-6) = $\frac{5}{-4}$ (x - 4)

Distribute $\frac{5}{-4}$  into the terms inside the parenthesis:

y + 6 = $\frac{ 5}{-4}x$  + 5  

  Subtract 6 from both sides to isolate y:

y + 6 - 6 = $-\frac{ 5}{4}x$ +5 - 6

The equation of the line in slope-intercept form is:

$y = -\frac{ 5}{4}x - 1$