Question

Pleas help I need within the next 10 min

Answer 1

Qn 5:

• Slope = (4 - (-2))/(3 - (-1)) = 6/4 = 3/2.

We have y - 4 = (3/2)(x - 3).

=> y = (3/2)x - 1/2.

Qn 6:

We have y - (-3) = -9(x - (-1)).

Qn 7:

We have y - 8 = (1/3)(x - (-2)).

Answer 2

5. Slope-intercept form:

`\sf y = (3)/(2) x + (1)/(2)`

6. Point-slope form:

`\sf y + 3 = -9(x +1)`

7. Point-slope form:

`\sf y - 8 = (1)/(3)(x + 2)`

Explanation:

5. To find the slope of the line, we use the following formula:

`\sf m = (y_2 - y_1)/(x_2 - x_1)`

where
`\sf (x_1, y_1) :(-1,-2)` and
`\sf (x_2, y_2):(3,4)` are two points on the line.

In this case, we have:

`\sf m = (4 - (-2))/(3 - (-1)) = (6)/(4) =(3)/(2)`

Therefore, the slope of the line is 3/2.

To find the y-intercept, we can substitute one of the points into the slope-intercept form of the equation of a line:

y = mx + b

Substituting (-1, -2) into the equation, we get:

`\sf -2 = (3)/(2)(-1) + b`

Solving for b, we get:

`\sf b = (1)/(2)`

Therefore, the equation of the line in slope-intercept form is:

`\sf y = (3)/(2) x + (1)/(2)`

6. To find the equation of the line in point-slope form, we use the following formula:

`\sf y - y_1 = m(x - x_1)`

where
`\sf (x_1, y_1): (-1,-3)` is a point on the line and m is the slope of the line(m) = -9.

In this case, we have:

`\sf y - (-3) = -9(x - (-1))`

`\sf y + 3 = -9(x +1)`

Therefore, the equation of the line in point-slope form is:

`\sf y + 3 = -9(x +1)`

7. To find the equation of the line in point-slope form, we use the same formula as in the previous problem.

`\sf y - y_1 = m(x - x_1)`

where
`\sf (x_1, y_1): (-2,8)` is a point on the line and m is the slope of the line(m) = 1/3.

In this case, we have:

`\sf y - 8 = (1)/(3)(x + 2)`

Therefore, the equation of the line in point-slope form is:

`\sf y - 8 = (1)/(3)(x + 2)`