Answer:
The figure is attached down
Step-by-step explanation:
To graph a line you must have its equation
The form of the linear equation is y = m x + b, where
- m is its slope
- b is the y-intercept (y at x = 0)
∵ The slope of the line is [tex]-\frac{2}{3}[/tex]
∴ y = [tex]-\frac{2}{3}[/tex] x + b
- To find b substitute x and y in the equation by the coordinates
of a point on the line
∵ The line passing through point (-5 , -4)
∴ x = -5 and y = -4
∵ -4 = [tex]-\frac{2}{3}[/tex] (-5) + b
∴ -4 = [tex]\frac{10}{3}[/tex] + b
- Subtract [tex]\frac{10}{3}[/tex] from both sides
∴ [tex]-\frac{22}{3}[/tex] = b
∴ y = [tex]-\frac{2}{3}[/tex] x - [tex]\frac{22}{3}[/tex]
To draw the line substitute x by any two values and find their ys
∵ x = -2
∴ y = [tex]-\frac{2}{3}[/tex] (-2) - [tex]\frac{22}{3}[/tex]
∴ y = -6
∴ The line passing through point (-2 , -6)
∵ x = 1
∴ y = [tex]-\frac{2}{3}[/tex] (1) - [tex]\frac{22}{3}[/tex]
∴ y = -8
∴ The line passing through point (1 , -8)
∵ x = 4
∴ y = [tex]-\frac{2}{3}[/tex] (4) - [tex]\frac{22}{3}[/tex]
∴ y = -10
∴ The line passing through point (4 , -10)
Now we can make a table to draw the line
→ x : -5 : -2 : 1 : 4
→ y : -4 : -6 : -8 : -10
Plot the points on the graph paper and draw the line
Look to the attached graph
