Final Answer:
The equation with a slope of 1 is a) y = 5x - 5. It directly displays a slope of 5, confirming its coefficient of x represents the slope.
Thus the option is a) y = 5x - 5 is correct answer.
Step-by-step explanation:
The slope of a linear equation in the form y = mx + b represents the coefficient of x, 'm'. Here, in equation 'a', y = 5x - 5, the coefficient of x is 5, indicating the slope. Slope-intercept form (y = mx + b) directly displays the slope ('m') and the y-intercept ('b'). In this case, the slope ('m') is 5, indicating that for every unit change in x, y changes by 5 units.
To further confirm the slope, you can rewrite equation 'a' in the slope-intercept form, y = mx + b. The given equation y = 5x - 5 already matches this form, where 'm' (the slope) is 5.
Equation 'b' is in point-slope form (y - y₁ = m(x - x₁)), not in the slope-intercept form, so it requires manipulation to determine the slope. Equations 'c' and 'd' are not in the slope-intercept form, and determining their slope requires conversion into y = mx + b form, where the coefficient of x will represent the slope.
Therefore, equation 'a) y = 5x - 5' is the one with a slope of 1 because its coefficient of x (5) represents the slope in the slope-intercept form of a linear equation.