Question

Plot the line for the equation on the graph. y − 6 = −37(x − 2)

Answer 1

The equation
`\(y - 6 = -37(x - 2)\)` describes a linear relationship with a slope of -37. See the graph attached.

When expanded and simplified, the equation becomes
`\(y = -37x + 74 - 6\)`, which further simplifies to
`\(y = -37x + 68\)`.

This is a downward-sloping line with a y-intercept at (0, 68) and a slope of -37. The line crosses the y-axis at 68, indicating the initial y-value when x is zero. As x increases, y decreases at a rate of 37 units for each unit increase in x.

The graph is a straight line, illustrating a consistent and negative linear relationship between x and y.