Answer:
The equation is y = [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
The slope-intercept form of the linear equation is y = m x + b, where
- m is the slope of the line
The rule of the slope of a line is [tex]m=\frac{y2-y1}{x2-x1}[/tex] , where
- (x1, y1) and (x2, y2) are two points lie on the line
To find the equation that represents the given table choose two ordered pairs from it
∵ Points (4, 6) and (6, 7) are from the table
∴ x1 = 4 and y1 = 6
∴ x2 = 6 and y2 = 7
→ Substitute them in the rule of the slope to find it
∵ [tex]m=\frac{7-6}{y6-4}=\frac{1}{2}[/tex]
∴ m = [tex]\frac{1}{2}[/tex]
→ Substitute it in the form of the equation above
∴ y = [tex]\frac{1}{2}[/tex] x + b
→ To find b substitute x and y in the equation by the coordinates
of any points from the table
∵ x = 4 and y = 6
∴ 6 = [tex]\frac{1}{2}[/tex] (4) + b
∴ 6 = 2 + b
→ Subtract 2 from both sides
∴ 6 - 2 = 2 - 2 + b
∴ 4 = b
→ Substitute its value in the equation above
∴ y = [tex]\frac{1}{2}[/tex] x + 4
∴ The equation is y = [tex]\frac{1}{2}[/tex] x + 4
