Question

Find a point on the line and the lines slope

y+3=-2(x+4)
point on the line: ( , )
slope:

Answer 1

Point on the line: (-4, -3)

Slope: -2

Explanation:

The point-slope form of a linear equation is:

`\large\boxed{y-y_1=m(x-x_1)}`

where:

• m is the slope
• (x₁, y₁) is a point on the line.

If we compare the given equation y + 3 = -2(x + 4) to the point-slope formula, we can see that:

• m = -2
• x₁ = -4
• y₁ = -3

Therefore, the slope (m) of the given line is -2, and the (x₁, y₁) point on the line is (-4, -3).

Note: The values of x₁ and y₁ are subtracted in the point-slope formula, yet the corresponding values in the given equation are positive. This means that the values of x₁ and y₁ in the given equation should be negative, since subtracting a negative value results in a positive number.

Answer 2

Point on the line: (0,-11)

Slope: -2

Explanation:

To find a point on the line y+3=-2(x+4), we can simply substitute a value for x and solve for y.

In this case, if we substitute x = 0, we get:

y + 3 = -2 ( 0 + 4)

y + 3 = - 8

y = -11

Therefore, one point on the line is (0,-11).

To find the slope of the line, we can rewrite the equation in slope-intercept form: y = mx + c

y+3=-2(x+4)

Distribute -2.

y + 3 = -2x - 8

Subtract 3 on both sides:

y + 3 - 3 = -2x - 8 - 3

y = -2x - 11

Comparing this equation with y = mx + c.

we get

m = -2.

The slope of the line is the coefficient of the x term, which in this case is -2.

Therefore, the slope of the line is -2, and the point on the line is (0,-11).