Write an equation in slope-intercept form when the slope and a point are given.
The slope-intercept form of the equation is nothing but the equation of a line, in the form of its slope and intercept it makes with the y-axis.
Answer: The equation of a line can be written as y = y1 + m ( x - x1) when slope m and a point (x1, y1) are given.
Let the given slope be m, and the known point be (x1, y1)
The general equation of a line in slope-intercept is given by y = mx + c, where m is slope of the line and c is the y-intercept.
Using the given slope and the point, and using the above-given slope-intercept equation of the line to calculate the only unknown i.e. intercept c.
y = mx + c ----- (1)
⇒ y1 = m.x1 + c
⇒ c = y1 - m.x1
Using this value in equation (1) we get,
⇒ c = y-intercept = y1 - mx1
⇒ y = y1 + m ( x - x1)