Question

complete the table with ordered pairs that give the coordinates of points that lie on the line shown in the graph
x -1 2.6
y 5.5

Explanation:

Step1: Find the slope - intercept form of the line

Assume the line is $y = mx + b$. Pick two points on the line, say $(0, 3)$ and $(1,5)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5 - 3}{1-0}=2$. Using the point - slope form with the point $(0,3)$ (so $b = 3$), the equation of the line is $y=2x + 3$.

Step2: Find $y$ when $x=-1$

Substitute $x=-1$ into $y = 2x+3$. Then $y=2\times(-1)+3=1$.

Step3: Find $x$ when $y = 5.5$

Substitute $y = 5.5$ into $y=2x + 3$. We get $5.5=2x+3$. Solving for $x$:
$2x=5.5 - 3=2.5$, so $x = 1.25$.

Step4: Find $y$ when $x = 2.6$

Substitute $x = 2.6$ into $y=2x+3$. Then $y=2\times2.6+3=5.2 + 3=8.2$.

Answer:

$x$	$y$
1.25	5.5
2.6	8.2