Find an equation of the line that satisfies the given conditions
Through (5,2) and slope 3
To find the equation of a line given a point and a slope, we can use the point-slope form of a linear equation, which is:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
In this case, the given point is (5,2) and the slope is 3. Substituting these values into the point-slope form, we have:
y - 2 = 3(x - 5)
Expanding the equation:
y - 2 = 3x - 15
To isolate y, we can add 2 to both sides:
y = 3x - 13
Therefore, the equation of the line that satisfies the given conditions is y = 3x - 13.
To find the equation of a line given a point and slope, you can use the point-slope form of a linear equation.
The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
In this case, the given point is (5, 2) and the slope is 3.
Plugging these values into the point-slope form, we get:
y - 2 = 3(x - 5)
Now, we can simplify this equation:
y - 2 = 3x - 15
To get the equation in slope-intercept form (y = mx + b), we can further simplify by adding 2 to both sides:
y = 3x - 15 + 2
y = 3x - 13
Therefore, the equation of the line that satisfies the given conditions is y = 3x - 13.