Question

5-14 Find an equation of the line that satisfies the given conditions. Express the equation in slope-intercept form. 5. Slope 3, y- ercept - 2 6. Slope y- intercept 4 2/5 7. Through (2, - 3) , slope 6 8. Through (-3,-5),s] slope a - 7/2 9. Through (2, 1) and (1, 6) 10. Through (- 1, - 2) and (4, 3) 11. Through (4, 84) and (13, - 312) 12. Through (6, 70) and (16, 300) 13. x-intercept 1, y- rcept - 3

Answer 1

To create an equation in slope-intercept form, we need the slope and y-intercept. For a given slope and y-intercept, the equation is directly written as y = mx + b. When provided with points, we calculate the slope and then establish the full equation.

Step-by-step explanation:

To write an equation of a line in slope-intercept form, which is y = mx + b, we need two pieces of information: the slope (m) of the line and the y-intercept (b). The y-intercept is the point where the line crosses the y-axis, and the slope indicates the steepness of the line.

For instance, if the slope is 3 and the y-intercept is -2, the equation in slope-intercept form would be y = 3x - 2. Similarly, if the slope is 2/5 and the y-intercept is 4, the equation becomes y = (2/5)x + 4.

To find the equation of a line that passes through two points, like (2, 1) and (1, 6), we would first calculate the slope using the formula m = (y2 - y1) / (x2 - x1), which in this case would give us a slope of -5. The equation can then be written using the slope and one of the points to solve for the y-intercept.

Answer 2

Slope-intercept form: y = mx + b [m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y)]

5. Since you know:

m = 3

b = -2 Plug it into the equation

y = mx + b

y = 3x - 2

6. Do the same as #5

7. m = 6 and (2, -3) Plug in m

y = 6x + b To find b, plug in the point (2, -3)

-3 = 6(2) + b

-3 = 12 + b Subtract 12 on both sides

-15 = b

y = 6x - 15

8. Do the same as #7

9. To find the slope, use the slope formula:

`m=(y_2-y_1)/(x_2-x_1)` and plug in the two points

(2, 1) = (x₁, y₁)

(1, 6) = (x₂, y₂)

`m=(6-1)/(1-2) =(5)/(-1)`

m = -5

y = -5x + b To find b, plug in either one of the points, I will use (1, 6)

6 = -5(1) + b Add 5 on both sides

11 = b

y = -5x + 11

10. Do the same as #9, should be y = x - 1

11. Do the same as #9 and #10, should be y = -44x + 260

12. Do the same as #9-11, should be y = 23x - 68

13. x-intercept is the point where the line crosses through the x-axis, or the x value when y = 0 ---> (x, 0)

You know:

x-intercept: (1, 0) and y-intercept: (0, -3) [(1, 0) is (x₂, y₂)]

Do the same as #9-12 to find the slope

You should get y = 3x - 3