Question

Write an equation in slope-intercept form of a line that has a slope of 1/2 and goes through the ordered pair (-6, 7).

Answer 1

$\large\underline{\bold{Given- }}$

• A lline that has a slope of 1/2 and goes through the ordered pair (-6, 7).

$\large\underline{\bold{To \: Find - }}$

• The equation of line

$\large\underline{\bold{Solution-}}$

Concept Used :-

We know,

• The equation of line having slope 'm' and makes an intercept 'c' on y axis is given by

• y = mx + c.

Here,

• Slope of line, m = 1/2.

• Let intercept on y- axis be 'c'

then

• equation of line is given by

$\rm :\longmapsto\:y \: = \: \dfrac{1}{2} x + c - - - (1)$

Since,

• Equation (1) passes through the point (- 6, 7),

So,

$\rm :\longmapsto\:7 = \dfrac{1}{2} \times ( - 6) + c$

$\rm :\longmapsto\:7 = - 3 + c$

$\rm :\longmapsto\:c \: = \: 10$

So,

• equation (1) can be rewritten as

$\rm :\longmapsto\:y \: = \: \dfrac{1}{2} x \: + \: 10$

Additional Information :-

Additional Information Different forms of equations of a straight line

1. Equations of horizontal and vertical lines

• Equation of the lines which are horizontal or parallel to the X-axis is y = a, where a is the y – coordinate of the points on the line.
• Similarly, equation of a straight line which is vertical or parallel to Y-axis is x = a, where a is the x-coordinate of the points on the line

2. Point-slope form equation of line

• Consider a non-vertical line L whose slope is m, A(x,y) be an arbitrary point on the line and P(a, b) be the fixed point on the same line. Equation of line is given by y - b = m(x - a)

3. Slope-intercept form equation of line

• Consider a line whose slope is m which cuts the Y-axis at a distance ‘a’ from the origin. Then the distance a is called the y– intercept of the line. The point at which the line cuts y-axis will be (0,a). Then equation of line is given by y = mx + a.

4. Intercept Form of Line

• Consider a line L having x– intercept a and y– intercept b, then the line passes through  X– axis at (a,0) and Y– axis at (0,b). Equation of line is given by x/a + y/b = 1.

5. Normal form of Line

• Consider a perpendicular from the origin having length p to line L and it makes an angle β with the positive X-axis. Then, equation of the line is given by x cosβ + y sinβ = p.