# 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 (x_{1}, y_{1})

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)

⇒ y_{1} = m.x_{1} + c

⇒ c = y_{1} - m.x_{1}

Using this value in equation (1) we get,

⇒ c = y-intercept = y_{1} - mx_{1}

⇒ y = y_{1} + m ( x - x_{1})

Thus, the equation of a line can be written as y = y_{1} + m ( x - x_{1})

## 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 = y_{1} + m ( x - x_{1}) when slope m and a point (x_{1}, y_{1}) are given.

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