Write the equation of the line, with the given properties, in slope -intercept form. Slope =-4, (-8,7)
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.
Given: Slope = -4 and a point on the line (-8, 7)
To find the equation, we need to find the value of b, the y-intercept.
Using the point-slope form of a line, we have:
(y - y₁) = m(x - x₁)
Substituting the values, we get:
(y - 7) = -4(x - (-8))
Simplifying:
y - 7 = -4(x + 8)
y - 7 = -4x - 32
y = -4x - 32 + 7
y = -4x - 25
Therefore, the equation of the line with the given properties, in slope-intercept form, is y = -4x - 25.
To write the equation of a line in slope-intercept form, y = mx + b, we need to find the slope (m) and the y-intercept (b).
Given the slope (m) = -4 and the point (-8, 7), we can substitute these values into the equation:
y - y₁ = m(x - x₁)
Plugging in the values:
y - 7 = -4(x - (-8))
Simplifying:
y - 7 = -4(x + 8)
Expanding the equation:
y - 7 = -4x - 32
Now, we isolate y by adding 7 to both sides:
y = -4x - 32 + 7
Simplifying further:
y = -4x - 25
Therefore, the equation of the line in slope-intercept form is y = -4x - 25.
To write the equation of a line given its slope and a point, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) are the coordinates of the given point.
In this case, the slope (m) is -4, and the given point is (-8,7). Plugging these values into the point-slope form, we get:
y - 7 = -4(x - (-8))
Simplifying further:
y - 7 = -4(x + 8)
Now, let's distribute the -4 to the terms inside the parentheses:
y - 7 = -4x - 32
To obtain the slope-intercept form (y = mx + b), we need to isolate y. Add 7 to both sides of the equation:
y = -4x - 32 + 7
Simplifying:
y = -4x - 25
Therefore, the equation of the line, with the given properties, in slope-intercept form is y = -4x - 25.