Question

Can you guys help me with this

Answer 1

C

Explanation:

The point-slope form of the equation of a line passing through the point (x1, y1)with a slope of m is given by:

y - y1 = m(x - x1)

To find the equation of the line passing through the point (-5, 7)with a slope of -4/3, we substitute m = -4/3, x1 = -5, and y1 = 7 into the point-slope form equation:

y - 7 = (-4/3)(x - (-5))

Simplifying this equation, we get the final result in slope-intercept form:

y = (-4/3)x + (17/3)

Therefore, the equation of the line in a point-slope form that passes through (-5,7) and has a slope of -4/3 is y + 7 = -4/3 (x + 5)

Answer 2

C

Explanation:

Recall the point-slope form of a linear equation:

`y-y_(1)=m(x-x_(1) )`

Where y1 and x1 are points from the ordered pair (x1, y1),

and m represents the slope of the line.

We are given that the point (-5, 7) belongs to the graph. Here, the x-coordinate is -5, and the y-coordinate is 7.

Let's plug in these values, were x1=-5, and y1=7:

`y-y_(1)=m(x-x_(1) )=\\y-7=m(x-(-5))=\\y-7=m(x+5)`

We are also given that the slope is -4/3.

In other words, m=-4/3. Let's plug this value in:

`y-7=m(x+5)=\\y-7=-(4)/(3)(x+5)`

Thus, the answer is C.