Write an equation of the line given the following information. Write the answer in slope-intercept form if possible.
The slope is -2, and the line passes through the point (6,-8).
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
From the given information, the slope is -2 and the line passes through the point (6, -8). We can use this information to find the equation of the line.
Using the point-slope form of a linear equation, which is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line, we can substitute in the given values:
y - (-8) = -2(x - 6)
y + 8 = -2(x - 6)
Now, we can simplify and convert the equation to slope-intercept form:
y + 8 = -2x + 12
Subtract 8 from both sides:
y = -2x + 4
Therefore, the equation of the line, in slope-intercept form, is y = -2x + 4.
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 slope (m) is -2 and the line passes through the point (6, -8), we can substitute these values into the slope-intercept form equation.
Using the point-slope form, we have:
(y - y1) = m(x - x1)
Substituting the values, we have:
(y - (-8)) = -2(x - 6)
Simplifying, we get:
y + 8 = -2(x - 6)
Expanding the expression, we have:
y + 8 = -2x + 12
Moving the terms around, we get:
y = -2x + 12 - 8
Simplifying further, we find:
y = -2x + 4
Therefore, the equation of the line in slope-intercept form is y = -2x + 4.
To write an equation of a line, we can use the point-slope form or the slope-intercept form.
1. Point-Slope Form
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1),
where (x1, y1) represents a point on the line, and m represents the slope of the line.
In this case, the slope (m) is given as -2, and the line passes through the point (6, -8). So we can substitute these values into the point-slope form:
y - (-8) = -2(x - 6).
Simplifying, we have:
y + 8 = -2x + 12.
Now, we can rewrite this equation in slope-intercept form.
2. Slope-Intercept Form
The slope-intercept form of a linear equation is given by:
y = mx + b,
where m represents the slope of the line, and b represents the y-intercept.
To convert the equation from point-slope form to slope-intercept form, we need to solve for y.
Starting with the point-slope equation:
y + 8 = -2x + 12,
subtracting 8 from both sides, we get:
y = -2x + 4.
Now, we have the equation of the line in slope-intercept form. The equation is:
y = -2x + 4.