Write an equation in slope-intercept form when the slope and a point are given.

Solution:

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.

Slope decides the nature and the angle line makes with the x-axis, while intercept tells the point of cut it makes with the y-axis.

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)

Thus, the equation of a line can be written as y = y₁ + m ( x - x₁)

Write an equation in slope-intercept form when the slope and a point are given.

Summary:

The equation of a line can be written as y = y₁ + m ( x - x₁) when slope m and a point (x₁, y₁) are given.