How do you find slope, point slope, slope intercept, standard form, domain and range of a line for Line J (-3,4) (0,10)?

Question

Abigail Allen · Accepted Answer

#"Slope " = 2, "Point - Slope form " y - 10 = 2x#

#"Slope - intercept form is " y = 2x + 10#

#"Standard form " 2x - y = -10#

#"Domain and Range " -oo to =oo#

#(x_1, y_1) = (-3,4), (x_2, y_2) = (0,10)#

#"1. Slope " m = (y_2 - y_1) / (x_2 - x_1) = (10-4) / (0 + 3) = 2#

#"2. Point - Slope form is " (y - y_1) = m (x - x_1)#

#(y - 10) = 2 * (x - 0) " or " y - 10 = 2x#

#"3. Slope - intercept form is " y = 2x + 10#

#"4. Standard form is " 2x - y = -10#

#"5. Domain is " - oo to +oo#

#"6. range is " - oo to +oo#

Eli Assouline · Answer

undefined To find the slope of a line, use the formula: slope (m) = (change in y) / (change in x).

For the given points (-3,4) and (0,10):
Change in y = 10 - 4 = 6
Change in x = 0 - (-3) = 3

Slope (m) = 6 / 3 = 2

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

Using point (-3,4) and slope m = 2:
y - 4 = 2(x - (-3))

To find the slope-intercept form, use the formula: y = mx + b, where m is the slope and b is the y-intercept.

Using point (-3,4) and slope m = 2:
y = 2x + b
Substitute (-3,4) into the equation to solve for b:
4 = 2(-3) + b
b = 4 + 6 = 10

The equation in slope-intercept form is y = 2x + 10.

To find the standard form of a line, rearrange the slope-intercept form: Ax + By = C.

Using the equation y = 2x + 10:
2x - y = -10

The equation in standard form is 2x - y = -10.

The domain of a line is all real numbers (-∞, ∞) and the range depends on the slope.

For line J, domain: (-∞, ∞)
Range: (-∞, ∞)