Slope Intercept help please!?

Question

 

Write an equation in slope-intercept form (y=mx+b) for the line that satisfies each set of conditions.And please dont just give me the answers, can you please explain how you got it too? Thank you :)

1)Slope of -2/3 and passing through the point (6, -1)

2)slope 1/2, passes through (6,4)

3)slope of -2 and passing through the point (-1,-2)

4)passing through the points ( 2,3) & ( 4,9)

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Answer 1

1).  Given that slope(m) = -2/3, and point (x, y) = (6, -1)

The 'slope-intercept' form is y=mx + b

Substitute m = -2/3 and (x, y) = (6, -1) in the slope-intercept form.

-1 = (-2/3)(6) + b.

-1 = (-2)(2) + b

-1 = -4 + b

Add 4 to each side.

b = 3.

Substitute m = (-2/3) and b = 3 in the slope-intercept form.

y = (-2/3)x + 3.

Therefore the 'slope-intercept' form is y = (-2/3)x + 3.

Answer 2

2).  Given that slope(m) = 1/2, and point (x, y) = (6, 4)

The 'slope-intercept' form is y=mx + b

Substitute m = 1/2 and (x, y) = (6, 4) in the slope-intercept form.

4 = (1/2)(6) + b.

4 = (3) + b

Subtract 3 from each side.

b = 1.

Substitute m = (1/2) and b = 1 in the slope-intercept form.

y = (1/2)x + 1.

Therefore the 'slope-intercept' form is y = (x/2) + 1.

Answer 3

3).  Given that slope(m) = -2, and point (x, y) = (-1, -2)

The 'slope-intercept' form is y=mx + b

Substitute m = -2 and (x, y) = (-1, -2) in the slope-intercept form.

-2 = (-2)(-1) + b.

-2 = (2) + b

Subtract 2 from each side.

b = -4.

Substitute m = 2 and b = -4 in the slope-intercept form.

y = (-2)x - 4.

Therefore the 'slope-intercept' form is y = - 2x - 4.

Answer 4

4). Given that points are (2, 3) and (4, 9)

Slope formula: m = (y₂ - y₁) / (x₂ - x₁)

m = (9 - 3)/(4 - 2)

m = 6/2 = 3.

Slope(m) = 3, and point (x, y) = (2, 3)

The 'slope-intercept' form is y=mx + b

Substitute m = 3 and (x, y) = (2, 3) in the slope-intercept form.

3 = (3)(2) + b.

3 = (6) + b

Subtract 6 from each side.

b = -3.

Substitute m = 3 and b = -3 in the slope-intercept form.

y = (3)x - 3.

Therefore the 'slope-intercept' form is y = 3x - 3.