A line has a slope if and passes through the point (-1, -8) write its equation in slope intercept form
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If a line has a slope `m` and passes through the point (`x₁`, `y₁`), then its equation in slope-intercept form is:
y = mx + (y₁ - mx₁)
In this case, the given slope is `m`. The point it passes through is (-1, -8), so `x₁ = -1` and `y₁ = -8`. Substituting these values into the equation:
y = mx + (-8 - m(-1))
y = mx - 8 + m
y = mx + m - 8
This is the equation of the line in slope-intercept form.
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 that the line has a slope of 'm' and passes through the point (-1, -8), we can use the point-slope form of a line to find the equation.
The point-slope form of a line is: y - y1 = m(x - x1), where (x1, y1) represents the given point.
In this case, (-1, -8) represents the given point, so we substitute these values into the point-slope form:
y - (-8) = m(x - (-1))
Simplifying further, we get:
y + 8 = m(x + 1)
To convert this equation into slope-intercept form (y = mx + b), we need to isolate 'y'.
Let's start by simplifying the equation:
y + 8 = mx + m
Next, we will move the constant term (8) to the other side of the equation:
y = mx + m - 8
Simplifying further gives:
y = mx - 8 + m
Now, combining similar terms:
y = mx + (m - 8)
Finally, we can see that the equation is now in slope-intercept form (y = mx + b), where b = (m - 8).
If a line has a slope `m` and passes through the point (`x₁`, `y₁`), then its equation in slope-intercept form is given by:
y - y₁ = m(x - x₁)
In this case, the given slope is `m`. The point it passes through is (-1, -8), so `x₁ = -1` and `y₁ = -8`. Substituting these values into the equation:
y - (-8) = m(x - (-1))
y + 8 = m(x + 1)
This is the equation of the line in slope-intercept form.