Question

What is the slope of the line that goes through the following two points?



(-5,-2) , (-8,7)

Answer 1

Question #4 - Rewriting a Linear Equation
Write the slope-intercept form of the equation for the given line:



6x+3y=-6

Answer 2

Question #5 - Write the equation given Slope and a Point
Write the equation of the line that goes through the point (2,5) with a slope of 2.

Answer 3

Question #9: Interpret a Linear Function
The graph of the function y=−
1
2​x+5 is:

Answer 4

To find the slope of the line passing through the two points (-5,-2) and (-8,7), we can use the slope formula:

m = (y2 - y1) / (x2 - x1)

Let's label the first point as (x1, y1) and the second point as (x2, y2):

(x1, y1) = (-5, -2)
(x2, y2) = (-8, 7)

Now we can substitute the values into the slope formula:

m = (7 - (-2)) / (-8 - (-5))

Simplifying the numerator and denominator:

m = (7 + 2) / (-8 + 5)
m = 9 / (-3)
m = -3

Therefore, the slope of the line passing through (-5,-2) and (-8,7) is -3.

Answer 5

To rewrite the equation in slope-intercept form (y = mx + b), we need to isolate y on one side of the equation.

Starting with the given equation:
6x + 3y = -6

Let's begin by subtracting 6x from both sides:
3y = -6 - 6x

Next, we divide both sides by 3 to solve for y:
y = (-6 - 6x) / 3

Simplifying the right side of the equation:
y = -2 - 2x

Therefore, the slope-intercept form of the equation is y = -2x - 2.

Answer 6

To write the equation of a line given a slope and a point, we can use the point-slope form:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope.

Given that the point is (2, 5) and the slope is 2, we substitute the values into the point-slope form:

y - 5 = 2(x - 2)

Now, let's simplify the equation and solve for y:

y - 5 = 2x - 4

y = 2x - 4 + 5

y = 2x + 1

Therefore, the equation of the line that goes through the point (2, 5) with a slope of 2 is y = 2x + 1.

Answer 7

The graph of the linear function y = -1/2x + 5 is a straight line. The negative coefficient (-1/2) indicates that the line has a negative slope. The slope is the change in y divided by the change in x, meaning that for every one change in x, the y-value decreases by 1/2.

The y-intercept of the line is (0, 5), which means that the line intersects the y-axis at y = 5. This indicates that when x is 0, y is equal to 5.

Since the coefficient of x is negative, the line slopes downward from left to right. As x increases, y decreases.

Overall, the line starts at y = 5 when x = 0 and decreases as x increases, with a slope of -1/2.

Please note that without a specific graph or pair of x and y values, it is not possible to provide an actual visualization of the graph.