Question

Find the slope between the points: (-3,-2) & (5,2) 2. Find the x-intercept: y = 6x+24

3. Create the equation in slope-intercept form of the line that passes through the point
4. Create the equation in slope-intercept form of the line that passes through the points (-3,-5) & (5,27)

Answer 1

1.
`(1)/(2)`

2. (-4, 0)

4. y = 4x + 7

Explanation:

1.

`(x_(1), y_(1))` = (-3, -2)

`(x_(2), y_(2))` = (5, 2)

Slope =
`(y_(2)-y_(1) )/(x_(2)-x_(1))`

=
`(2--2)/(5--3)`

=
`(2+2)/(5+3)`

=
`(4)/(8)`

=
`(1)/(2)`

2.

y = 6x + 24

The line crosses the x axis when y = 0, so:

0 = 6x + 24

6x = - 24

x =
`(-24)/(6)`

= -4

(x, y) = (-4, 0)

3.

Question incomplete.

4.

Equation format:

y = mx + c

[m = the slope]

[c = the y-intercept]

`(x_(1), y_(1))` = (-3, -5)

`(x_(2), y_(2))` = (5, 27)

Slope =
`(y_(2)-y_(1) )/(x_(2)-x_(1))`

=
`(27--5)/(5--3)`

=
`(27+5)/(5+3)`

=
`(32)/(8)`

m = 4

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

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

y + 5 = 4 (x + 3)

= 4x + 12

y = 4x + 7

Answer 2

4x + 7.

Explanation:

1. Find the slope between the points: (-3,-2) & (5,2)

To find the slope between two points, we can use the formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) represent the coordinates of the two points.

In this case, we have (-3, -2) and (5, 2). Plugging these values into the formula, we get:

slope = (2 - (-2)) / (5 - (-3))

slope = 4 / 8

slope = 1/2

So, the slope between the points (-3,-2) and (5,2) is 1/2.

2. Find the x-intercept: y = 6x+24

To find the x-intercept, we set y to zero and solve for x. In other words, we find the value of x when the graph crosses or intersects the x-axis.

In this equation, y = 6x + 24. Setting y to zero, we get:

0 = 6x + 24

Let's solve for x now:

6x = -24

x = -4

Therefore, the x-intercept of the equation y = 6x + 24 is -4.

3. Create the equation in slope-intercept form of the line that passes through the point (-3,-5)

To create the equation in slope-intercept form (y = mx + b) of a line, we need the slope (m) and the y-intercept (b), which is the point at which the line crosses or intersects the y-axis.

Since we only have one point (-3,-5), we cannot directly calculate the slope. However, we can use the slope formula we mentioned earlier, along with another point that lies on the line, to determine the slope.

Let's assume another point on the line is (x, y).

Using the slope formula, we have:

m = (y - (-5)) / (x - (-3))

Now, let's plug in the coordinates of the given point (-3,-5):

m = (y + 5) / (x + 3)

We can simplify this equation to find the slope.

To find the y-intercept, we can use the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Plugging in (-3,-5) as the point, we have:

y - (-5) = m(x - (-3))

y + 5 = m(x + 3)

Now, we can rearrange this to the slope-intercept form (y = mx + b):

y = mx + 3m - 5

So, the equation in slope-intercept form for the line passing through the point (-3,-5) is y = mx + 3m - 5.

4. Create the equation in slope-intercept form of the line that passes through the points (-3,-5) and (5,27)

Similar to the previous problem, we'll use the slope formula to find the slope (m) between the two given points.

The slope formula:

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

Plugging in the coordinates of the two points (-3,-5) and (5,27), we have:

m = (27 - (-5)) / (5 - (-3))

m = 32 / 8

m = 4

Now, we can use the point-slope form of a line (y - y1 = m(x - x1)) to find the equation of the line.

Using the point (-3,-5):

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

y + 5 = 4(x + 3)

Finally, let's rewrite this equation in slope-intercept form (y = mx + b):

y = 4x + 12 - 5

y = 4x + 7

Therefore, the equation in slope-intercept form for the line passing through the points (-3,-5) and (5,27) is y = 4x + 7.